A new approach to numerical simulation of two-phase, two-dimensional flows (sprays or two-phase jets), based on a combination of the full Lagrangian method for the dispersed phase and the mesh-free vortex blob method for the carrier phase, is suggested. The problem of calculation of all parameters in both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases. This allows one to study in detail local zones of particle accumulation in complex transient flows, including those with multiple intersections of particle trajectories and the formation of "folds" in the concentration field of the dispersed phase. The new approach is applied to modelling of the time evolution of a two-phase Lamb vortex and the development of an impulse two-phase jet. These examples involve the formation of local zones of particle accumulation and regions of multiple intersections of particle trajectories. The correct simulation of these flow features is expected to involve serious difficulties when the conventional Eulerian/Lagrangian methods, described in the literature, are used.